Liverpool closed the gap on leaders Manchester City with victory over West Ham, while Chelsea tightened their grip on third place in Saturday's Premier League action.
The Blues saw off Burnley 4-0 at Turf Moor, a scoreline that was matched by Aston Villa in their statement victory against Southampton.
Newcastle United, Crystal Palace and Brentford also picked up wins, but it was a bad start to life under new management for Leeds in their early kick-off against Leicester City.
Following another eventful day of Premier League action, Stats Perform delves into the key Opta facts from each of the games.
Leeds United 0-1 Leicester City: New manager, same Leeds
Jesse Marsch's first game as Leeds boss ended in defeat to Leicester as United fell to a fifth successive league loss for the first time since April 2015, when they were in the Championship.
Leeds have failed to score in three straight league matches for the first time in a year, this despite registering 19 shots in their latest blank against Leicester.
United's expected goals (xG) return of 1.95 is their highest without scoring in a league game since June 2020, and the familiar failings were also on show at the other end.
Harvey Barnes' second-half winner means Leeds have gone 13 league games without a clean sheet, their longest-such run since 14 without a shutout ending in August 2016.
This was the fifth straight league game Barnes has scored against Leeds – four of those while playing for Leicester and one for West Brom, making them his favourite opponent.
Aston Villa 4-0 Southampton: Coutinho's home comforts
Villa are firmly back on track after registering back-to-back victories under Steven Gerrard for the first time since his opening two games in charge in November.
The Villans put four unanswered goals past Southampton at Villa Park for their biggest Premier League win since thrashing Liverpool 7-2 in October 2020.
Barcelona loanee Philippe Coutinho once again played a big part in the victory by scoring one and assisting another for Douglas Luiz.
Coutinho has now been directly involved in six goals in his first four home league games for Villa, scoring three of his own and setting up as many.
Ollie Watkins had earlier opened the scoring with his 21st Premier League strike since the start of the 2020-21 season, while Danny Ings added to his two assists with Villa's fourth goal.
Newcastle United 2-1 Brighton and Hove Albion: Fraser helps end Magpies' duck against Seagulls
For a while things looked incredibly bleak for Newcastle, even after their big-money takeover, but they now find themselves seven points above the relegation zone.
The Magpies held off Brighton to make it eight Premier League games without defeat – no team is on a better such run – with five of those matches ending in victory.
Ryan Fraser opened the scoring to make it two goals in five Premier League outings, matching his tally from his previous 70 appearances, before setting up Fabian Schar.
That was the earliest United have scored twice in a Premier League home game since January 2007 and, despite Lewis Dunk's header, Eddie Howe's side saw out the win.
It marks the first time Newcastle have defeated Brighton in the Premier League in their 10th such encounter, having previously failed to so much as score against them at home.
Norwich City 1-3 Brentford: Bees buzzing thanks to Toney treble
After a run of eight Premier League games without a win, Brentford bolstered their survival ambitions with a well-earned victory away at bottom side Norwich.
Ivan Toney was the hero for the Bees with three goals, two of those from the penalty spot, making Brentford the 40th different team to boast a hat-trick scorer.
The Brentford striker now has nine Premier League goals for the season, each of those coming via his right foot.
Teemu Pukki scored a consolation but it was another miserable day for Norwich, whose goal difference of -42 is the worst at this stage since Derby County in 2007-08 (-44).
Not that it will matter a great deal in the grand scheme of things, but Brentford are the first team Pukki has scored home and away against in a single Premier League season.
Wolves 0-2 Crystal Palace: Shaky Wanderers lose again
Wolves' European hopes suffered another blow as they fell to a third successive Premier League defeat, as many as they lost in their previous 13.
Bruno Lage's out-of-form side have now conceded six goals in their last four league games, after shipping just five in 12 before that.
Jean-Philippe Mateta came up with the breakthrough from close range for his fourth goal in eight Premier League starts, and Wilfried Zaha doubled Palace's lead from the penalty spot.
Ivory Coast international Zaha has now been directly involved in 83 goals in the competition, the joint-ninth best total for an African player, level with Nwankwo Kanu.
With this latest loss, it is the first time Wolves have lost three games in a row against Palace in their entire league history.
Burnley 0-4 Chelsea: Blues cruise at Turf Moor
It was business as usual for Chelsea as they won for a third Premier League game running without conceding in what proved to be a straightforward victory at lowly Burnley.
The Blues scored all four of their goals in the second half as they enjoyed their biggest away league win since October 2018 when also beating Burnley by the same scoreline.
This was the biggest margin of victory for an away side in a game that was goalless at half-time since Tottenham beat Aston Villa 4-0 in December 2012.
Reece James started the scoring and in the process became the first defender from Europe's top five leagues to both score and assist five goals this term in all competitions.
Kai Havertz also netted twice before Christian Pulisic added some gloss to the scoreline – his fourth goal at Turf Moor, matching a record for an away player set by Tottenham's Harry Kane.
Liverpool 1-0 West Ham: Reds roll on thanks to Mane
Sadio Mane's first-half goal made it seven wins in a row for Liverpool in the Premier League, their best such streak since a run of 18 when they claimed the title two years ago.
That close-range finish was Mane's 12th of the season in the league, nine of those coming at Anfield – no player has scored more home goals in the division this season.
Trent Alexander-Arnold played the ball into the box for Mane's goal for his 16th assist in all competitions this term, more than he has ever registered in a single campaign.
Liverpool were not at their best and that was particularly true of Mohamed Salah, who failed to score from six shots – only against Stoke in April 2018 (seven) has he fared worse.
Incredibly, Virgil van Dijk has never been on the losing side for Liverpool in 60 Premier League home games at Anfield, setting a new record in that regard.
Frank praises Brentford's pressing, sees no tactical revamp with Toney departure
Thomas Frank heaped praise on Brentford's pressing following their 3-1 victory over Southampton on Saturday.
Bryan Mbeumo scored twice from Brentford's forwards forcing the Southampton backline into errors as the Bees earned their second Premier League win of the season.
This did not go unnoticed by Frank, who believes his side rank as one of the best in the league when it comes to that specific aspect.
He told BBC Sport: "They made errors because we pressed them unbelievably well. I think we are one of the best teams to do the high pressure in the Premier League.
"The players are so committed and that is the reason why we capitalised on errors from Southampton.”
Despite the departure of Ivan Toney to Al-Ahli, Frank does not think their style of play will have to be restructured too much, with both Mbuemo and Yoane Wissa enjoying productive starts to the season in his absence.
Frank said: “Ivan is a fantastic player, I'd love to have him in the team but he has his own journey and is going elsewhere.
"Our style of play hasn't changed. Wissa and Ivan are different players but the style doesn't change.”
Southampton boss Russell Martin was frustrated with his side’s mistakes at crucial moments, believing their performance was far better than the scoreline suggested.
He said to the BBC: “We made two mistakes that we were punished for, which is frustrating and disappointing.
"I saw lots of good things to feel positive about. I feel a lot better this week than I did after the Nottingham Forest game.”
Guardiola has 'no words' for hat-trick hero Haaland
Pep Guardiola was lost for words to describe Erling Haaland after his eighth Premier League hat-trick fired Manchester City to a 3-1 victory over West Ham.
Having scored a treble to help City claim a 4-1 win over Ipswich Town on matchday two, Haaland did likewise on Saturday to keep them perfect as they edged out the Hammers at the London Stadium.
Haaland's seven goals this season are the most any player has ever netted in the first three matches of a Premier League campaign, while only Sergio Aguero (12), Alan Shearer (11) and Robbie Fowler (nine) have ever helped themselves to more match balls in the competition.
Across English football's top four tiers, he is also the first player to score two hat-tricks in a team's first three games of a league season since Bradford City's Paul Jewell in 1994-95.
The Norwegian has now scored more than once in 26% of his Premier League matches (18/69, eight hat-tricks, 10 braces), leaving Guardiola in disbelief.
"There are no words for him," Guardiola told BBC Sport.
"All we can do is make him play better and better and give him as many balls as possible into the box. It's what we have to do. We are there and we added quality.
"This is a team. When you have to run backward, no one asks who has to do it. Everyone has to. When we see Erling doing that, it is fantastic."
Haaland himself, meanwhile, believes having an extended pre-season due to Norway missing out on Euro 2024 has helped him start the season in peak condition.
"I feel good. I feel energised. I had a long vacation and a long pre-season. I'm feeling good," Haaland told City's website.
"The years here have gone quick and it's been going like, 'bam bam bam', now I have a little bit of rest in my body and my feet. I feel really good now and I'm ready for more.
"I feel more refreshed and more energised. So when you do that you can practice on things you want to become better at in training. I feel good. I want to become better. I'm happy."
City sit top of the early-season table with nine points from nine available and saw last season's runners-up Arsenal slip up on Saturday, drawing 1-1 with Brighton and Hove Albion.
Haaland, though, feels it is too early to think about the title race, adding: "They [City's rivals] haven't slipped up yet. Three games, nine points. This is a great start.
"But let's not think too far ahead, because there’s potentially 70 games left this season. Let's breathe a bit and take it game by game."
Lopetegui rues missed opportunity as West Ham lose to Man City
West Ham manager Julen Lopetegui was not encouraged by the performance of his team despite losing 3-1 at home to Manchester City in their third league game.
“It is true that City is one of the best teams around the world for sure… but it is also true too that in the second half we have been very close to a draw,” he said speaking to BBC Match of the Day.
“I think we have played one very good second half. The start has been very good for us too.”
West Ham threatened for extended periods of the match and had chances to level the match at 2-1 down, with the best coming from Mohammed Kudus as he smashed a shot against the bar in the second half.
They also started the game brightly before going a goal down inside 10 minutes.
“In my mind we started very well, being aggressive,” said Lopetegui.
“We know in this plan normally they have initiative, it’s very difficult to not concede initiative then. That’s why you have to do a lot of very good things to overcome them.
“In the second half we had chances, I think we kept the ball much more, much more, and didn't concede a lot of chances."
But the hosts were ultimately undone by the brilliant finishing of Erling Haaland, who scored his second hat-trick in as many matches.
“He is one of the best players in the world, that's why he plays for Manchester City,” he said.
“You have to compete with these kind of players. City has the power and the quality to create chances.”
But ultimately, he was left frustrated at the sense of a missed opportunity and that his team were unable to earn themselves a draw that hadn’t seemed implausible during the match.
“Today I think the first goal was a pity for us but I’ve said it. I was happy with the performance think we were able to draw but again they damage us,” he said.
“Against this kind of team, if you make a mistake they don’t forgive. This is the difference they have… A little mistake they punish you, they punish us.
“We have to improve, to know to compete against this kind of team to be close to perfection.
“Don't make mistakes, be calm, defend well… we have quality players too.”
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